Abstract
It has been realized that synchronization using linear feedback control method is efficient compared to nonlinear feedback control method due to the less computational complexity and the synchronization error. For the problem of feedback synchronization of Duffing chaotic system, in the paper, we firstly established three-dimensional Duffing system by method of variable decomposition and, then, studied the synchronization of Duffing chaotic system and designed the control law based on linear feedback control and Lyapunov stability theory. It is proved theoretically that the two identical integer order chaotic systems are synchronized analytically and numerically.
Highlights
In recent years, the chaotic control has become one of the important research fields of nonlinear science and received the attention of many scholars around the world
An efficient nonlinear control method has been applied to the synchronization of unified chaotic systems using the Lyapunov method in [4] and a nonlinear control scheme for the synchronization has been presented using the Lyapunov stability theory in [5]
Based on the threedimensional Duffing system and the theory of Lyapunov equation of system stability judgment, the linear state feedback synchronization in Duffing chaotic system is studied in this paper
Summary
The chaotic control has become one of the important research fields of nonlinear science and received the attention of many scholars around the world. The problem of controlling chaos for new dynamical system has been studied and the sufficient conditions for synchronization of chaotic systems have been derived in [3]. The synchronization process of a four-dimensional chaotic system by using linear feedback controller, single variable, and adaptive controller methods has been proposed and demonstrated in [7]. Synchronization of energy resource systems has been proposed when the parameters of the master system are unknown and different from the slave system using adaptive linear feedback control in [8]. The chaos synchronization between two different chaotic systems can be realized based on the nonlinear feedback control method in [17]. Based on the threedimensional Duffing system and the theory of Lyapunov equation of system stability judgment, the linear state feedback synchronization in Duffing chaotic system is studied in this paper. −1.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 x Figure 1: 2D Duffing chaotic system phase diagram
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